Working with exponential growth and logarithmic relationships
Simplify: 2³ × 2⁴
When multiplying same bases, add the exponents: a^m × a^n = a^(m+n)
Solve: 2^x = 16
Rewrite 16 as power of 2: 16 = 2⁴, so x = 4
Convert to logarithmic form: 10³ = 1000
a^b = c is equivalent to logₐc = b
Simplify: log₂8 + log₂2
logₐb + logₐc = logₐ(b×c), so log₂(8×2) = log₂16 = 4
Solve: log₅x = 2
logₐb = c means a^c = b, so 5² = 25